[Shankhadeep Bose]

Let’s assume the two numbers in the ratio 7:12 are 7x and 12x, where x is a common multiplier.

According to the given condition, when 7 is added to the first number and 2 is added to the second number, the new ratio becomes 21:31.

So, after adding 7 to the first number, it becomes 7x + 7, and after adding 2 to the second number, it becomes 12x + 2.

Now, we can set up the equation based on the new ratio:

(7x + 7) / (12x + 2) = 21/31

To eliminate the fractions, after cross-multiplying:

(7x + 7) * 31 = (12x + 2) * 21

217x + 217 = 252x + 42

Subtracting 217x from both sides, we get:

217 = 35x + 42

Subtracting 42 from both sides, we get:

175 = 35x

Dividing both sides by 35, we get:

x = 5

Now, we can find the values of the two numbers:

First number = 7x = 7 * 5 = 35; Second number = 12x = 12 * 5 = 60

Answer: The two numbers are 35 and 60.